On Admissible Constellations of Consecutive Primes
نویسندگان
چکیده
2 . Admissible constellations . Let us start with a formal definition : al, 122, . . ., ak is an admissible sequence of integers if the ai's do notform a complete set of residues mod p for any prime p.-Clearly only the primes p 5 k have to be considered . A sequence which is not admissible is called inadmissible . Beginning with the admissible sequence (ai) we now search for constellations of integers (x+ai), with all its members prime . We shall call such a sequence an admissible constellation .-According to our definition, the sequence (0, 2,4) leading to the constellation (x, x+2, x+4) and being represented by the primes 3, 5, 7, is inadmissible, since precisely one of three consecutive even or odd integers is divisible by 3 . This implies that 3, 5, 7 and -7, -5, -3 are the only instances for which all members of the constellation are primes. On the other hand, the sequence (0, 2, 6, 8), leading to the quadruplet
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عنوان ژورنال:
- BIT
دوره 28 شماره
صفحات -
تاریخ انتشار 1988